Linearized Learning Methods with Multiscale Deep Neural Networks for Stationary Navier-Stokes Equations with Oscillatory Solutions

In this paper, we present linearized learning methods to accelerate the convergence of training for stationary nonlinear Navier-Stokes equations. To solve the stationary nonlinear Navier-Stokes (NS) equation, we integrate the procedure of linearization of the nonlinear convection term in the NS equation into the training process of multi-scale deep neural network approximation of the NS solution. Four forms of linearizations are considered. After a benchmark problem, we solve the highly oscillating stationary flows utilizing the proposed linearized learning with multi-scale neural network for complex domains. The results show that multiscale deep neural network combining with the linearized schemes can be trained fast and accurately.